A method to evaluate the influence of the laser linewidth on the linearly frequency-modulated(LFM)signals generated by heterodyning two free-running laser diodes(LDs)is proposed.The Pearson correlation coefficient bet...A method to evaluate the influence of the laser linewidth on the linearly frequency-modulated(LFM)signals generated by heterodyning two free-running laser diodes(LDs)is proposed.The Pearson correlation coefficient between the instantaneous frequency of the generated LFM signal and that of an ideal LFM signal is introduced to quantify the quality of the generated LFM signal.The closed-form solution of the correlation coefficient is given,which shows that the correlation coefficient is determined by the ratio of the LFM signal bandwidth to the square root of the total linewidth of the two LDs when the observation interval is fixed.Simulation results are also given,which proves the correctness of the theoretical results.展开更多
Let A,B be associative rings with identity,and(S.≤)a strictly totally ordered monoid which is also artinian and finitely generated.For any bimodule AaMB. we show that the bimodule [[A^(S.≤)]][M^(S.≤)][[B^(S.≤)]]de...Let A,B be associative rings with identity,and(S.≤)a strictly totally ordered monoid which is also artinian and finitely generated.For any bimodule AaMB. we show that the bimodule [[A^(S.≤)]][M^(S.≤)][[B^(S.≤)]]defines a Morita duality if and only if _AM_B defines a Morita duality and A is left noetherian.B is right noetherian.As a corollary,it.is shown that the ring[[A^(S.≤)]]of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule _AM_B such that B is right noetherian.展开更多
A classical question of Yoneda asks when the tensor product of two injective modules is injective. A complete answer to this question was given by Enochs and Jenda in 1991. In this paper the analogue question for pure...A classical question of Yoneda asks when the tensor product of two injective modules is injective. A complete answer to this question was given by Enochs and Jenda in 1991. In this paper the analogue question for pure-injective modules is studied.展开更多
基金supported by the National Key R&D Program of China(No.2017YFE0121500)the National Natural Science Foundation of China(Nos.61971193 and 61601297)+1 种基金the Open Fund of State Key Laboratory of Advanced Optical Communication Systems and Networks,Peking University,China(No.2020GZKF005)the Fundamental Research Funds for the Central Universities。
文摘A method to evaluate the influence of the laser linewidth on the linearly frequency-modulated(LFM)signals generated by heterodyning two free-running laser diodes(LDs)is proposed.The Pearson correlation coefficient between the instantaneous frequency of the generated LFM signal and that of an ideal LFM signal is introduced to quantify the quality of the generated LFM signal.The closed-form solution of the correlation coefficient is given,which shows that the correlation coefficient is determined by the ratio of the LFM signal bandwidth to the square root of the total linewidth of the two LDs when the observation interval is fixed.Simulation results are also given,which proves the correctness of the theoretical results.
基金supported by National Natural Science Foundation of China(10171082)Foundation for University Key Teacherthe Ministry of Education(GG-110-10736-1001)
文摘Let A,B be associative rings with identity,and(S.≤)a strictly totally ordered monoid which is also artinian and finitely generated.For any bimodule AaMB. we show that the bimodule [[A^(S.≤)]][M^(S.≤)][[B^(S.≤)]]defines a Morita duality if and only if _AM_B defines a Morita duality and A is left noetherian.B is right noetherian.As a corollary,it.is shown that the ring[[A^(S.≤)]]of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule _AM_B such that B is right noetherian.
文摘A classical question of Yoneda asks when the tensor product of two injective modules is injective. A complete answer to this question was given by Enochs and Jenda in 1991. In this paper the analogue question for pure-injective modules is studied.
